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Banking 273 12 Banking 12.1 INTRODUCTION All of us need money to meet our day-to-day expenses. We earn money, spend money and also, save some money. We would like to keep the money in safe custody. Banks are the institutions where we keep the money in the form of deposits and those who need money can borrow as loans on payment of interest with certain conditions. Besides this, banks also help the people in various kinds of financial transactions. Some of the functions of a bank are : 1. Keeping money of the depositors and pay interest on deposits. 2. Giving loans to the borrowers on interest. 3. Buying and selling security bonds. 4. Receiving payments – Telephone bills, Electricity bills, water bills, school fees etc. 5. Transferring money from one place to another. 6. Collection of taxes – income tax, sales tax, house tax etc. 7. Issuing/Encashing travellers cheques in Local/Foreign currency. 8. Providing All Time Money (ATM) facility to the customers. 9. Issuing credit cards. 10. Exchange of Foreign currency etc. For the convenience of customers, the banks offer different types of accounts (deposits) some of which are : (i) Savings Bank Account (ii) Current Account (iii) Fixed deposit Account. (iv) Recurring deposit Account. 274 Mathematics 12.2 OBJECTIVES After studying this lesson, the learner will be able to : state different types of accounts. calculate interest for a saving bank account, given the rate of interest. calculate interest/maturity value of fixed/term deposit given the rate of interest compounded yearly, semi-annually or quarterly (not more than four conversion periods). 12.3 EXPECTED BACKGROUND KNOWLEDGE (i) Knowledge of simple interest when principal (P), rate of interest (R) and time (T), for which money was invested are given i.e. S.I. = PRT. (ii) Compound interest when P, R, n are given i.e., C.I. = A – P where A = P(1 + R)n, n is number of conversion periods. 12.4 TYPES OF ACCOUNTS You can open different types of accounts in a bank depending upon your needs. Some of these are : (a) Savings bank account (b) Fixed or term deposit account (c) Current account 12.4.1 Savings Bank Account This is the most popular account offered by the banks. This account encourages people to develop the habit of saving. Anybody can open this account with a minimum sum of Rs 1000 with cheque book facility. In this account, deposits and withdrawals can be made and the record is maintained by the bank in a ‘Pass-Book’ given to the Account holder (i.e. the person who holds the account). The bank pays interest for the money that an account holder keeps in the account. The prevailing rate of interest is 4% per annum compounded half yearly. The rate of interest changes from time to time. On opening a savings bank account, a pass book is issued to the account holder. It contains date wise entries of deposits withdrawals and the interest earned. It bears savings bank account number also. The general format of a page of the savings bank passbook is as given below : Banking 275 Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P — — — — — — — — — — — — — — — Money can be withdrawn from the bank through a withdrawal slip (sample shown) or by a cheque (sample shown below). Fi.g 12.1 Sample of Withdrawal slip Fig. 12.2 Sample of Cheque Note : In a savings bank account, (i) The bank pays interest for the month on the minimum closing balance from the 10th day of the month to the last day of the month. (ii) The interest is credited to the account every six months. (iii) The present rate of interest is 4% per annum compounded semi-annually. (iv) Usually not more than 25 withdrawals are allowed in a quarter from Savings Bank account. 276 Mathematics 12.4.2 Computation of Interest (i) Write down the minimum balance between the closing balance on 10th to the last day of the month. (ii) Add all the minimum balances for each month as per step (i) to obtain principal for one month. (iii) Calculate the simple interest on this sum for one month using the formula 1 Interest = P × R × 12 where P is Principal, R is rate of interest per annum and time 1 month i.e. 1/12 year. (iv) If account is opened after the 10th day of month, no interest is payable for that month. (v) No interest is paid for the month in which the account is closed. Let us illustrate the above with some examples. Example 12.1 : Sidharth opened a savings bank account in State Bank of India on 5th March 2003 with a deposit of Rs 5000. He deposited Rs 1500 on 10th March 2003 and withdrew Rs 3000 on 29th March, 2003. Find the principal for which he will earn interest for March 2003. Solution : Balance on 5th March, 2003 = Rs 5000 Balance on 10th March, 2003 = Rs 6500 Balance on 29th March, 2003 = Rs 3500 Here minimum balance between 10th and 31st March, 2003 = Rs 3500. Therefore, the principal for which interest is earned for the month of March 2003 is Rs 3500. Example 12.2 : Anisha’s savings bank account pass-book has the following entries : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 Jan 6 By Cash — 20000.00 20000.00 Feb 11 By Cash — 10000.00 30000.00 April 5 By Cheque — 5000.00 35000.00 April 27 To Cheque 18000.00 — 17000.00 May 3 By Cash — 13000.00 30000.00 June 15 To Cheque 20000.00 — 10000.00 Find the sum on which Anisha will earn interest from January to June 2002. Banking 277 Solution : The qualifying amount for the interest is the minimum balance between the 10th and the last day of the month. Principal for January = Rs 20000 Principal for February = Rs 20000 Principal for March = Rs 30000 Principal for April = Rs 17000 Principal for May = Rs 30000 Principal for June = Rs 10000 Total Rs 127000 Thus, the sum on which Anisha will earn interest for one month = Rs 127000. Example 12.3 : Ritus’s pass book has the following entries : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 Jan. 1 B/F — — 12000.00 Jan. 9 To Cash Rs 7000.00 — 5000.00 Jan. 11 By Cheque — 20000.00 25000.00 Feb. 10 To Cheque Rs 10000.00 — 15000.00 April 3 By Cash — 5000.00 20000.00 June 5 By Cheque — 10000.00 30000.00 June 25 By Cheque — 5000.00 35000.00 If the rate of interest is 4% per annum, find the interest earned by Ritu at the end of June on her savings bank account. Solution : Details of qualifying amount for the calculation of interest are as below: Month Amount Jan. Rs 5000.00 Feb. Rs 15000.00 March Rs 15000.00 April Rs 20000.00 May Rs 20000.00 June Rs 30000.00 Total Rs 105000.00 278 Mathematics 1 Here P = Rs 105000, R = 4% and T = year. 12 105000 × 4 × 1 ∴ Interest = PRT = Rs = Rs 350. 100 × 12 ∴ Interest earned by Ritu = Rs 350. Example 12.4 : Ashok has a savings bank account in a bank. His passbook has the following entries: Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 July 11 By cash — 6000.00 6000.00 Aug 12 By Cheque — 4000.00 10000.00 Sept 5 By Cheque — 10000.00 20000.00 Sept 21 To Cheque 8000.00 — 12000.00 Nov 9 By Cheque — 8000.00 20000.00 Dec 10 By Cheque — 10000.00 30000.00 Dec 29 To cash 26000.00 — 4000.00 The account is closed on 3rd January 2003. Find the amount received by Ashok, if the rate of interest is 4% per annum. Solution. Details of qualifying amount for the calculation of interest are : Month Amount July Rs — August Rs 6000.00 September Rs 12000.00 October Rs 12000.00 November Rs 20000.00 December Rs 4000.00 Total Rs 54000.00 1 Here P = Rs 54000, R = 4% and T = year 12 LM 54000 × 4 × 1OP ∴ Interest = PRT = Rs N 100 × 12 Q = Rs 180.00 ∴ Amount received = Rs (4000 + 180) = Rs 4180. Banking 279 Example 12.5 : The dates and respective balances in the pass book of David’s savings bank account are given below : Dates Balances 2002 October 5 Rs 1500.00 October 25 Rs 3500.00 December 8 Rs 5000.00 2003 January 11 Rs 8000.00 February 5 Rs 6000.00 February 9 Rs 10000.00 February 11 Rs 7500.00 March 15 Rs 20000.00 March 29 Rs 10000.00 Calculate the interest earned upto March 2003 if the rate of interest is 4% per annum. Solution : Details of qualifying amount for the calculation of interest are : Month Amount Oct, 2002 Rs 1500 Nov, 2002 Rs 3500 Dec, 2002 Rs 5000 Jan, 2003 Rs 5000 Feb, 2003 Rs 7500 March 2003 Rs 7500 Total Rs 30000 Here P = Rs 30000, R = 4% and T = 1/12 year 30000 × 4 × 1 ∴ Interest = PRT = Rs = Rs 100 100 × 12 ∴ Interest earned by David = Rs 100. 280 Mathematics Example 12.6 : Salim opened a savings bank account with a bank on 9th January 2002 with a cash deposit of Rs 10000. Subsequently he deposited Rs 2000 on the 8th day of every month. He withdrew Rs 3000 on 25th April and Rs 6000 on 28th June 2002. Write all entries of the passbook. If the bank pays interest at the rate of 4% per annum, calculate the interest upto the last day of 30th June 2002 and make the entry in the passbook alongwith the balance. Solution : The entries in the passbook are as below : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 9th Jan. By cash — 10000.00 10000.00 8th Feb. By Cash — 2000.00 12000.00 8th March By Cash — 2000.00 14000.00 8th April By Cash — 2000.00 16000.00 25th April To Cash 3000.00 — 13000.00 8th May By Cash — 2000.00 15000.00 8th June By Cash — 2000.00 17000.00 28th June To Cash 6000.00 — 11000.00 Details of qualifying amount for the calculation of interest are : Month January February March April May June Total Amount 10000 12000 14000 13000 15000 11000 75000 (in Rs) 75000 × 1 × 4 ∴ Interest upto 30th June, 2002 = Rs = Rs 250 100 × 12 The interest entry is made on 1–7–2002 as below : 1.7.2002 By Interest — 250.00 11250.00 CHECK YOUR PROGRESS 12.1 1. Krishna Murthy opened a savings bank account in State Bank of India on 7th July 2002. His pass book has the following entries : Banking 281 Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 7th July By cash — 1100.00 1100.00 11th July By Cash — 400.00 1500.00 25th August By Cash — 1000.00 2500.00 10th September By Cheque — 1500.00 4000.00 Calculate the principal for which he will earn interest for the months of July, August and September 2002, together. 2. The entries in the savings bank account pass book of Kamlesh are as under: Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 1st January B/F — — 15000.00 10th January By Cash — 5000.00 20000.00 9th February By Cheque — 5000.00 25000.00 9th March By Cash — 5000.00 30000.00 11th April By Cash — 5000.00 35000.00 25th June By Cheque — 5000.00 40000.00 Calculate the interest at the end of June 2002 at 4% per annum. 3. The entries in the passbook of a savings bank account holder who opened his account of 11th January 2002 are as follows : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 11th January By cash — 5000.00 5000.00 11th Feb. By Cheque — 5000.00 10000.00 9th March By Cheque — 5000.00 15000.00 6th June To Cheque 10000.00 — 5000.00 10th June By Cash — 15000.00 20000.00 26th June To Cash 16000.00 — 4000.00 282 Mathematics If the rate of interest is 4% per annum, find the interest earned if the account is closed on : (i) 30th June, 2002 (ii) 3rd July, 2002. 4. Madhu’s Savings Bank Account passbook has the following entries : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 July 1 B/F — — 6000.00 July 9 By Cheque — 4000.00 10000.00 Sept. 10 To Cheque 9000.00 — 1000.00 Sept. 14 By Cash — 4000.00 5000.00 December 5 By Cash — 4500.00 9500.00 December 10 By Cash — 1500.00 11000.00 December 23 To Cheque 9000.00 — 2000.00 If the rate of interest is 6% per annum, calculate the interest entry on 1st January 2003 in the passbook alongwith the balance. 5. A page from the pass book of savings bank account is given below : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P July 1, 2002 B/F — — 2000.00 July 11, 2002 By Cheque — 8000.00 10000.00 August 9, 2002 By Cheque — 10000.00 20000.00 November 25, 2002 To Cheque 15000.00 — 5000.00 December 19, 2000 By Cash — 15000.00 20000.00 The account is closed on 2nd January 2003. Find the amount received if the rate of interest is 4% per annum. 6. Kavita opens a savings bank account with a bank on 8th January, 2002 with a cash deposit of Rs 10000. Subsequently she deposited Rs 6000 on the 6th day of every month. She withdraws Rs 4000 on 3rd April and Rs 12000 on 10th June 2002. If the bank pays interest at the rate of 5% per annum, payable at the end of June and December, write all the entries, including interest, which are made upto 1st July 2002. Banking 283 12.4.3 Current Account In a saving bank account, the account holder is allowed to have a limited number of withdrawals in a half year. Big business concerns, companies, government organisations etc., have to do a number of transactions every day. For them banks offer a different type of account called current account. For this account, there is no limit on number of withdrawals or on the amount of withdrawals but the banks do not pay interest. Rather, sometimes, they charge some money as service charges. Here, the minimum balance for individuals account is Rs 5000 while for big concerns, it is Rs 10000. Depending upon the goodwill of the individual/company, banks allow the current account holder to get money over and above their deposits called overdraft. 12.4.4 Fixed Deposit Account Suppose you have some money which is not required for some time. The scheme suitable for depositing such money is the Fixed Deposit or Term deposit. Here the depositor agrees to keep the money with the bank for a fixed time. Obviously, the bank can use this money more freely than the money kept in the savings bank account. Hence the banks offer higher rates of interest on such deposits depending upon the period of deposits. The rate of interest per annum on term deposits is as below : (i) For 46 days and above but less than 179 days. 5% (ii) For six months and above but less than 1 year. 6% (iii) For one year and more. 6.5% For senior citizens, and additional interest of 0.5% is given on deposits. The total amount receivable after the expiry of the time is called maturity value. Example 12.7 : Anju deposited Rs 2920 in a fixed deposit scheme in a bank for 60 days. If the bank pays interest at 6% per annum, find the amount she receives at the end of 60 days. 60 Solution : Here P = Rs 2920, R = 6% per annum and T = year 365 FG 2920 × 6 × 60IJ ∴ Interest = PRT = Rs H 100 × 365 K = Rs 28.80 ∴ Amount Received by Anju = Rs (2920 + 28.80) = Rs 2948.80 Example 12.8 : Joginder makes a fixed deposit of Rs 31250 in a bank for 1½ years. If the rate of interest is 8% per annum compounded half yearly, find the maturity value of the money deposited by him. 284 Mathematics Solution : Note here that the interest for the first half year also forms a part of principal for the second half year and likewise for the third half years well. Thus, we shall make use of the formula for compound interest. 8 Here P = Rs. 31250, R = = 4% per half year 2 1 and T = 1 year = 3 Half years 2 ⇒ n = 3. ∴ Amount = P(1 + R)n = Rs 31250 1 + 4 100 FH IK 3 = Rs 35152 Maturity value of the deposit = Rs 35152 Example 12.9 : Amit makes a fixed deposit of Rs 31250 in a bank for 1½ years. If the rate of interest is 8% per annum compounded yearly, find the maturity value of the money deposited by him. 1 Solution : Here P = Rs 31250, R = 8%, T = 1 years. 2 FH 8 Amount after one year = Rs 31250 1 + 100 IK 1 and amount after 1 year 2 FH8 A = Rs 31250 1 + 100 IK FH1 + 100IK 4 = Rs 31250 × 1.08 × 1.04 = Rs 35100 Hence, the maturity value = Rs 35100. Note : Note the difference in the maturity value in Example 8 and Example 9. In example 8, the interest is compounded half yearly while in Example 9, the interest is compounded yearly. Example 12.10 : Kapil makes a fixed deposit of Rs 20000 in a bank in a year. If the rate of interest 8% per annum compounded quarterly, find the maturity value of the money deposited by him. Solution : Here P = Rs. 20000, R = 2% per quarter, Time = 4 quarters ∴ A = P(1 + R)n = Rs 20000 1 + 2 100 FH IK 4 = Rs 20000 × 1.02 × 1.02 × 1.02 × 1.02 = Rs 21648.64 Hence the maturity value = Rs 21649 (approx.) Banking 285 Example 12.11 : How much money should Nirmal deposit in a fixed deposit account in a bank so that she gets Rs 456976 after two years, the rate of interest being 8% per annum compounded half yearly. Solution : Here P = ?, A = Rs 456976, R = 4% per half year and T = 2 year = 4 half years i.e. n = 4 We know that A = P(1 + R)n ∴ FH 456976 = P 1 + 4 100 IK 4 FH IK = P 26 25 4 456976 × 25 × 25 × 25 × 25 P = Rs 26 × 26 × 26 × 26 = Rs 390625 Hence amount to be deposited = Rs 390625. CHECK YOUR PROGRESS 12.2 1. Find the amount at the end of 9 months if Rs 50000 is deposited and the interest 8% per annum is compounded quarterly. 2. Charu makes a fixed deposit of Rs 8000 in a bank for 1½ years. It the rate of interest is 10% per annum and the interest is compounded half yearly, find the maturity value of the money deposited by her. 3. Pankaj deposits Rs 75000 in a fixed deposit account for 3 years. If the rate of interest is 10% per annum compounded annually, find the maturity value of the money deposited by him. 4. How much money should Shanta deposit in a fixed deposit account in a bank so as to enable her to receive a sum of Rs 9261 after 1½ years, the rate of interest being 10% per annum compounded half yearly ? 5. How much money should Kamal deposit in a fixed deposit account in a bank so as to enable him to receive a sum of Rs 1061208 after nine months, the rate of interest being 8% per annum compounded quarterly ? LET US SUM UP There are different types of accounts in a bank. Some of these are : (i) Saving bank account (ii) Fixed or term deposit account (iii) Current account 286 Mathematics In a saving bank account : (i) the bank pays interest for the month on the minimum closing balance from the 10th day of the month to the last day of the month. (ii) the interest is credited to the account every six months. Step for computing interest are : (i) Write down the minimum balance between the closing balance on 10th to the last day of the month. (ii) Add all the minimum balances for each month as per step (i) to obtain principal for one month. (iii) Calculate the simple interest on this sum for one month using the formula 1 Interest = P × R × 12 where P is Principal, R is rate of interest per annum and time 1 month i.e. 1/12 year. (iv) If account is opened after the 10th day of month, no interest is payable for that month. (v) No interest is paid for the month in which the account is closed. TERMINAL EXERCISE 1. A page for the pass book of Mr. Dass’s Saving bank Account in a particular year is given below : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P Jan. 9 By Cash — 15000.00 15000.00 Feb. 10 By Cheque — 8000.00 23000.00 April 25 To Cheque 20000.00 — 3000.00 June 7 By Cash — 2000.00 5000.00 June 11 By Cash — 12000.00 17000.00 If the rate of interest is 4% per annum, find the interest earned by Mr. Dass at the end of June on his savings bank account. Banking 287 2. Sujata has a savings bank account in a bank. Her passbook has the following entries : Date Particulars Amount withdrawn Amount Deposited Balance Rs P Rs P Rs P 2002 July 1 B.F. — — 2500.00 July 9 By Cheque — 2500.00 5000.00 August 10 By Cash — 4000.00 9000.00 October 19 To Cheque 6000.00 — 3000.00 November 2 By Cash — 9600.00 12600.00 Dec. 20 To Cash 9200.00 — 3400.00 Dec. 27 By Cheque — 10600.00 14000.00 The account is closed on 10th January, 2003. Find the amount received if the rate of interest is 4% per annum. 3. Vandana makes a fixed deposit of Rs 62500 in a bank for 1½ years. If the rate of interest is 8% per annum compounded half yearly, find the maturity value of money deposited by her. 4. Smith makes a fixed deposit of Rs 10000 in a bank for a year. If the rate of interest is 8% per annum compounded quarterly, find the maturity value of the money deposited by her. 5. How much money should Sarla deposit in a fixed deposit account in a bank so that she gets Rs 194481 after two years, the rate of interest being 10% per annum compounded half-yearly ? 288 Mathematics ANSWERS Check Your Progress 12.1 1. Rs 6600 2. Rs 583.33 3. (i) Rs 166.66 (ii) Rs 180 4. Interest Rs 165, Balance Rs 2165 5. Rs 20240 6. Date Particulars Debit Credit Balance Rs P Rs P Rs P 2002 Jan. 5 By cash — 10000.00 10000.00 Feb. 6 By Cash — 6000.00 16000.00 March 6 By Cash — 6000.00 22000.00 April 3 To Cash 4000.00 — 18000.00 April 6 By Cash — 6000.00 24000.00 May 6 By Cash — 6000.00 30000.00 June 6 By Cash — 6000.00 36000.00 June 10 To Cash 12000.00 — 24000.00 July 1 By interest — 525.00 24525.00 Check Your Progress 12.2 1. Rs 53060.40 2. Rs 9261 3. Rs 99825 4. Rs 8000 5. Rs 1000000 Terminal Exercise 1. Rs 240 2. Rs 14140 3. Rs 70304 4. Rs 10824.32 5. Rs 160000

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